Problem: Solve for $x$ and $y$ using elimination. ${3x-6y = 3}$ ${-5x-5y = -50}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${15x-30y = 15}$ $-15x-15y = -150$ Add the top and bottom equations together. $-45y = -135$ $\dfrac{-45y}{{-45}} = \dfrac{-135}{{-45}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {3x-6y = 3}\thinspace$ to find $x$ ${3x - 6}{(3)}{= 3}$ $3x-18 = 3$ $3x-18{+18} = 3{+18}$ $3x = 21$ $\dfrac{3x}{{3}} = \dfrac{21}{{3}}$ ${x = 7}$ You can also plug ${y = 3}$ into $\thinspace {-5x-5y = -50}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(3)}{= -50}$ ${x = 7}$